Now Playing: Comparing Two Proportions (3:42)
One of the most basic and most common statistical comparisons is the comparison of two proportions. While the idea is very simple, the number of ways two proportions can be compared is remarkable. Proportions may be compared as a difference, a ratio, or an odds ratio. They may be compared using confidence intervals, inequality tests, non-inferiority tests, equivalence tests, or superiority by a margin tests. They may be compared using large-sample approximation formulas, or using exact distribution statistics. While all of these comparisons may be made using NCSS procedures, the purpose of this video is to familiarize you with a basic difference of two proportions analysis.
Suppose 1200 patients are assigned to an experimental treatment or a standard treatment such that there are 600 patients receiving each treatment. In the experimental treatment group, 427 of the 600 patients respond positively to the treatment, while in the standard treatment group, 386 respond positively.
To compare the two groups statistically in NCSS, we first open the Two Proportions procedure from the menu. Since we have the total number of patients in each group and the total number of successes, we select the first of the three types of data input.
While not required, it is convenient to change the labels to reflect the experiment.
We then enter the values of the table.
On the Summary Reports tab, we can leave the selections at the defaults.
On the Difference Reports tab, we’ll add the most basic Wald Z confidence interval.
We won’t include any Ratio Reports or Odds Ratio Reports.
We press the Run button to generate the analysis output.
A summary of the counts and the proportions is given in the first section of the report.
The second section shows the three specified confidence intervals of the difference. The three confidence intervals do not seem to differ much.
The third section shows the test of whether the two proportions differ statistically. The p-value of 0.0113 indicates the difference of about 0.07 to be statistically significant, although the confidence intervals of the previous section show a fairly wide range of values for the true difference.
The plots section at the end gives a visual representation of the counts and percentages for each group.